Question

The equation of the hyperbola referred to its axes as coordinate axes, whose latus rectum is 4 and eccentricity is 3 is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$e=3,2b^2/a=4\Rightarrow b^2=2a{e}^2=\frac{a^2+b^2}{a^2}\Rightarrow 9=\frac{a^2+2a}{a^2}\Rightarrow 9a=a+2\Rightarrow a=\frac{1}{4},b^2=\frac{1}{2}$

Equation of hyperbola is $16x^2-2y^2=1$